Monopoly Behavior

What do monopolists do? Generally we assume that a monopolist chooses the level of output to maximize profits.
As an accounting matter, profits (PR) are equal to total revenue (TR) minus total costs (TC):

PR = TR - TC

Profit will be maximized when the derivative of profit with respect to output (dPR/dQ) is equal to zero:

dPR/dQ = dTR/dQ - dTC/dQ = 0

Therefore, at the profit maximizing quantity, dTR/dQ (otherwise known as marginal revenue) must be equal to
dTC/dQ (marginal cost). In other words, the monopolist will choose the Q that makes MR=MC.

To solve a monopoly problem you will need to write down equations for TR and TC as functions of Q. Then differentiate
the two, set the resulting equations for MR and MC equal to each other, and solve for Q.